Unit 4 - Problem 10 ==> Generalized Equations

Given:

• Acceleration of gravity  = 9.8 m/s/s
• Mass of the object = 1 kilogram
• Height over ground = 50 meters
• G = 6.674 x 10^-11
• Radius of the earth = 6400 kilometers = 6,400,000 meters
• Mass of the earth = 5.97 x 10^24 kilograms

Calculate: Gravitational potential energy using mgh

• $$E_{potential} = m * g * h = 1 * 9.8 * 6400009 = 62720088.2$$

Calculate: Potential energy using (G*M1*M2)/r

• $$E_{potential} = G_{earth} * M_{object} * M_{earth}$$  
• $$E_{potential} = \left(\frac{6.674^{-11} * 1 * 5.97^{24}}{6400009}\right)$$
• $$E_{potential} = 6.225581870275496 * 10^-6 * 10^{-11} * 10^{24}$$
• $$E_{potential} = 6.225581870275496 * 10^7$$
• $$E_{potential} = 62255818.70275496$$

Calculate: Difference & % difference in two calculations

• $$E_{mgh} - E_{GM1M2/r} = difference$$
• $$62720088.2 - 62255818.70275496 = 464269.4972450435$$
• $$\left(\frac{difference}{E_{GM1M2/r}}\right) * 100 = percent_{difference}$$
• $$\frac{464269.4972450435}{62255818.70275496} * 100 = 0.745744746305133$$